This paper examines how return patterns evolve across major cryptocurrency groups using a functional data approach. Monthly log-returns of twenty liquid and widely traded assets are smoothed into continuous trajectories and compared with functional ANOVA across three common classifications: functional role, market capitalization, and consensus mechanism. The main result is that functional roles generate the most visible separation in return behavior. Smart Contract platforms show several months in which their average path diverges from Payment, DeFi and Layer 0 assets, especially around technology-driven events or periods of market stress. For market capitalization and consensus mechanism, differences appear occasionally but do not persist over time, and global L2 tests do not reject equality of mean curves. Overall, the evidence suggests that temporary divergence across coin classes is driven more by economic function than by size or validation method. These findings also illustrate how functional methods can track market segments that move together most of the time but separate during short, event-driven windows, which may be useful for monitoring structural changes in digital asset markets.
Balay et al. (Fri,) studied this question.